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Pade approximation is used to reduce the orders of the original system transfer functions in establishing the lumped circuit model of the transformer windings under very fast transient overvoltage (VFTO), but it can not guarantee the stability and accuracy of the reduced system. To address this issue, the transfer functions are firstly converted to state equations. Then one of Krylov-based subspace methods, Arnoldi algorithm, is presented to reduce the orders of the state equations in this paper. Finally the lumped element circuit model of transformer windings is established via the resulting order- reduced transfer functions by network synthesis method. The simulation results have proved that the accuracy becomes better and better with increasing the model orders, which Pade-based methods fail. It also demonstrates that the proposed approach is feasible and reliable for establishing lumped element equivalent circuit of transformer windings under VFTO.